For electronic component shopping Akihabara is not that good compared to a large on line store or the market district in Soeul Korea. Even so Akihabara is fun and if I only have a few hours in Tokyo that is where I head. For connectors and the like there is a little arcade on your left as you leave the busy station exit 90 degrees to the Yamanote line. The station is confusing as two train lines cross at right angles and there are several levels, most of the component stores are within 500m of the station. As for DIY stores there are a few tool stores specializing in small hand tools scattered around the district Tokyuu hands is one of the larger chains. take a compass and a map, the compass is invaluable just to determine which direction you are headed. Street signs are in both English and Japanese, addresses are by area making finding places from the address difficult. Enjoy your trip Japan is a fun place.

As Metalsculptor says the arcade just outside the station is the place for components, fun place each stall seems to have its own theme, IC's, transformers, connectors etc.
Go by train (the signs and announcements are in english as well)

Probably a bit late, but I was in Akihabara last month and it still has a lot of electronic components available, despite a lot of the stores now mainly catering for Japanese anime goods.

The following is from memory, as I can't remember exact locations, but hopefully it will help someone trying to navigate Akihabara.

The electronic parts market outside the station (easily identified by stores displaying and selling bright LEDs) has 2 floors consisting of various LEDs, connectors, transformers, screwdrivers, various components, DIY speaker parts/enclosures, ham radio parts and more.

The 2nd floor of the parts market contains a rental box showcase that people rent boxes and sell various goods in. There are several tube amplifier kits and a number of tubes for sale there.

There is also a general electronic store upstairs too.

If you leave the building and cross Chuuo road, if you walk straight, you will pass KFC on the left, if you progress straight a bit more, you can find the Rocket store which is a haven for ham radio parts such as antennas, transceivers and more.

Before the KFC on the left you'll see a small store called Oyaide Denki, that is a shop specialising in many cables including silver wire that you can use to make your own high end cables.

If you turn right at the KFC and then turn left into a small road at a later point, you will find some other popular electronics stores including Akizuki denki, Marutsu and Sengoku. These stores are general electronic stores and contain most of the parts you'll be after including opamps and more. They can be quite crowded though as they are popular stores.

Somewhere, nearby there is also another building that has several stories of electronic parts as well, but I've forgotten the exact location. It is similar to the electronic parts market outside the station. It has enclosures, tubes and many electronic parts. It is next door on the right of the Cospa store.

As for headphone/IEM stores, there is only one that I know of that is very good. It is called e-earphone and it's quite hard to find as it's in a small passageway of a building 5th floor next to an Akibao store in a small road between Chuuo road and the Mandarake building.

It has new and used headphones, IEMs, amps, DACs, tube amps, various hi-end cables and more at cheap prices. Pretty much all of the products have a sample that you can try, so you can compare IEMs, cables, amps and more. I only saw one amp kit available there for those only interested in DIY.